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Metrics and embeddings of generalizations of Thompson's group $F$

Author(s): J. Burillo; S. Cleary; M. I. Stein
Journal: Trans. Amer. Math. Soc. 353 (2001), 1677-1689.
MSC (2000): Primary 20F65; Secondary 20F05, 20F38, 20E99, 05C25
Posted: December 18, 2000
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Abstract:

The distance from the origin in the word metric for generalizations $F(p)$ of Thompson's group $F$ is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of $F(p)$. This interpretation of the metric is used to prove that every $F(p)$ admits a quasi-isometric embedding into every $F(q)$, and also to study the behavior of the shift maps under these embeddings.

References:

1.
Bieri, R. and Strebel, R., On groups of PL-homeomorphisms of the real line, Notes, Math. Sem. der Univ. Frankfurt, 1985.

2.
Brin, M.G. and Guzmán, F., Automorphisms of generalized Thompson groups, J. Algebra 203 (1) (1998), 285-348. MR 99d:20056

3.
Brown, K.S., Finiteness properties of groups, J. Pure App. Algebra 44 (1987), 45-75. MR 88m:20110

4.
Brown, K.S. and Geoghegan. R., An infinite-dimensional torsion-free $FP_{\infty }$ group, Invent. Math. 77 (1984), 367-381. MR 85m:20073

5.
Burillo, J., Quasi-isometrically embedded subgroups of Thompson's group $F$, J. Algebra 212 (1999), 65-78. MR 99m:20051

6.
Cannon, J.W., Floyd, W.J., and Parry, W.R., Introductory notes on Richard Thompson's groups, Enseign. Math. 42 (1996), 215-256. MR 98g:20058

7.
Cleary, S., Groups of piecewise-linear homeomorphisms with irrational slopes, Rocky Mountain J. Math. 25 (1995), 935-955. MR 97d:20040

8.
Fordham, S.B., Minimal Length Elements of Thompson's Group $F$, Thesis, Brigham Young University, 1995.

9.
Guba, V. and Sapir, M., Diagram Groups, Mem. Amer. Math. Soc. 130 (1997). MR 98f:20013

10.
Higman, G., Finitely presented infinite simple groups, Notes on Pure Math., vol. 8, Australian National University, Canberra, 1974. MR 51:13049

11.
Stein, M., Groups of piecewise linear homeomorphisms, Trans. Amer. Math. Soc. 332 (2) (1992), 477-514. MR 92k:20075

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Additional Information:

J. Burillo
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08192 Barcelona, Spain
Address at time of publication: Department of Applied Mathematics, University Politecnica de Catalunya, Campus Nord, Jordi Girona 1, 08034 Barcelona, Spain
Email: burillo@mat.upc.es

S. Cleary
Affiliation: Department of Mathematics, City College of CUNY, New York, New York 10031
Email: cleary@math0.sci.ccny.cuny.edu

M. I. Stein
Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
Email: mstein@mail.trincoll.edu

DOI: 10.1090/S0002-9947-00-02650-7
PII: S 0002-9947(00)02650-7
Received by editor(s): September 25, 1998
Received by editor(s) in revised form: August 11, 1999
Posted: December 18, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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